1 Purpose

nag_matop_complex_gen_matrix_actexp (f01hac) computes the action of the matrix exponential etA, on the matrix B, where A is a complex n by n matrix, B is a complex n by m matrix and t is a complex scalar.

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NW_SOME_PRECISION_LOSS

etAB has been computed using an IEEE double precision Taylor series, although the arithmetic precision is higher than IEEE double precision.

7 Accuracy

For a Hermitian matrix A (for which AH=A) the computed matrix etAB is guaranteed to be close to the exact matrix, that is, the method is forward stable. No such guarantee can be given for non-Hermitian matrices. See Section 4 of Al–Mohy and Higham (2011) for details and further discussion.

8 Parallelism and Performance

nag_matop_complex_gen_matrix_actexp (f01hac) is not threaded by NAG in any implementation.

nag_matop_complex_gen_matrix_actexp (f01hac) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

The matrix etAB could be computed by explicitly forming etA using nag_matop_complex_gen_matrix_exp (f01fcc) and multiplying B by the result. However, experiments show that it is usually both more accurate and quicker to use nag_matop_complex_gen_matrix_actexp (f01hac).

The cost of the algorithm is On2m. The precise cost depends on A since a combination of balancing, shifting and scaling is used prior to the Taylor series evaluation.

Approximately n2+2m+8n of complex allocatable memory is required by nag_matop_complex_gen_matrix_actexp (f01hac).